In this paper, distributed space-time (ST) codes for continuous-phase modulation (CPM) are introduced. The distributed ST codes are designed to operate in wireless networks containing a large set of nodes N, of which only a small a priori unknown subset S sub N will be active at any time. Under the proposed scheme, a relay node transmits a signal which is the product of a diagonal block-based ST code (optimized specifically for ST-CPM transmission) and a signature vector of length Nc uniquely assigned to each node in the network. An efficient method is presented for the design and optimization of appropriate signature vector sets, assuming a quasi-static, frequency nonselective fading channel model. If a properly designed signature vector set is employed it is shown that a diversity order of d = min{Ns,Nc} can be achieved, where Ns is the number of active relay nodes. The decoding complexity of the proposed scheme is shown to be independent of the number of active relay nodes, and non-coherent receiver implementations, which do not require channel estimation, are applicable. Compared to distributed ST transmission with linear modulation, distributed ST-CPM can considerably reduce the energy consumption at the transmitter due to the constant envelope of the transmit signal. At the same time, the additional energy consumption due to more complex receiver processing can be kept low. Therefore, the proposed distributed ST-CPM scheme is particularly apt for energy-efficient cooperative transmission in wireless networks.